Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 549 and 550 the smallest integer that is 301950 that is divisible by both numbers.
Least Common Multiple (LCM) of 549 and 550 is 301950.
LCM(549,550) = 301950
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 549 and 550. First we will calculate the prime factors of 549 and 550.
Prime Factorization of 549
3 | 549 |
3 | 183 |
61 | 61 |
1 |
Prime factors of 549 are 3,61. Prime factorization of 549 in exponential form is:
549 = 32×611
Prime Factorization of 550
2 | 550 |
5 | 275 |
5 | 55 |
11 | 11 |
1 |
Prime factors of 550 are 2, 5,11. Prime factorization of 550 in exponential form is:
550 = 21×52×111
Now multiplying the highest exponent prime factors to calculate the LCM of 549 and 550.
LCM(549,550) = 21×32×52×111×611
LCM(549,550) = 301950
Factors of 549
List of positive integer factors of 549 that divides 549 without a remainder.
1, 3, 9, 61, 183, 549
Factors of 550
List of positive integer factors of 550 that divides 550 without a remainder.
1, 2, 5, 10, 11, 22, 25, 50, 55, 110, 275, 550
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 549 and 550, than apply into the LCM equation.
GCF(549,550) = 1
LCM(549,550) = ( 549 × 550) / 1
LCM(549,550) = 301950 / 1
LCM(549,550) = 301950
(i) The LCM of 550 and 549 is associative
LCM of 549 and 550 = LCM of 550 and 549
1. What is the LCM of 549 and 550?
Answer: LCM of 549 and 550 is 301950.
2. What are the Factors of 549?
Answer: Factors of 549 are 1, 3, 9, 61, 183, 549. There are 6 integers that are factors of 549. The greatest factor of 549 is 549.
3. What are the Factors of 550?
Answer: Factors of 550 are 1, 2, 5, 10, 11, 22, 25, 50, 55, 110, 275, 550. There are 12 integers that are factors of 550. The greatest factor of 550 is 550.
4. How to Find the LCM of 549 and 550?
Answer:
Least Common Multiple of 549 and 550 = 301950
Step 1: Find the prime factorization of 549
549 = 3 x 3 x 61
Step 2: Find the prime factorization of 550
550 = 2 x 5 x 5 x 11
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 301950 = 2 x 3 x 3 x 5 x 5 x 11 x 61
Step 4: Therefore, the least common multiple of 549 and 550 is 301950.